{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(p):#模拟二分类信息熵\n",
    "    return -p * np.log(p)-(1-p)*np.log(1-p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u4XdTEvHcLaMhlwEf5p3A79/JR4uJa5GQc2IZIerE53sq8Lu382A0W5GRFIk1946Hv8pLdCwiu9w2Lg6vzB4HpZcc3xTpcP/an9FkNIuORXQOlhGiX3k/twwPrdsNs1XCjSkxePnuVKi9FaJjEfXIVcM1eOu3E+CrVGDbkWrc+8YuNBhYSMi5sIwQ/cJbOaVYuGEfJAm4K60//u+2FHhzjxlycZckhOHt+yYgQOWF3GNnMPv1n1DXbBIdi6gdf8oStXorpxSLPzsAALj/0oF4ZuZIyOVcQ4TcQ+qAULw7Nw1BPt7YXVaLu17biZpGo+hYRAB6WEZWrlyJ+Ph4qNVqpKWlITc397zH19bWYv78+YiOjoZKpcKQIUOwadOmHgUm6gtrd5wtIr+7LAGLZiRxMTNyO6P7BeP9uZcg1E+J/Sf1uPO1n1DbxEJC4tldRtavX4+srCwsWbIE+fn5SE5OxrRp01BZWdnp8UajEVdddRVKS0vx0Ucfobi4GKtXr0ZsbOxFhyfqDW9uP4Yln9uKyO+nJOKxa4exiJDbGh4TiPUPXIJwfyWKTukx+/VcDtmQcDLJztVw0tLSMH78ePznP/8BAFitVsTFxeEPf/gDHnvssXOOX7VqFf75z3/i4MGD8Pb27lFIvV6PoKAg1NXVITAwsEcfg6gzvxyamTc1EX+dNpRFhDzCIV09bn/VtoZOSlywbU6Jumc/o4m60t33b7uujBiNRuTl5SEjI+PsB5DLkZGRgZycnE5f8/nnnyM9PR3z58+HRqPByJEjsXTpUlgsvN+dxPrg53IWEfJYQzQBeOe+NAT7eqOgvBb3vrELjbzLhgSxq4xUV1fDYrFAo+m4J4dGo4FWq+30NSUlJfjoo49gsViwadMmPPHEE3jhhRfwzDPPdPl5DAYD9Hp9hwdRb/rfngo89vFeAMB9lw5kESGPNDwmEO/cl4ZAtRfyjtcg881daDbyF0VyvD6/m8ZqtSIyMhKvvvoqUlNTMWvWLCxatAirVq3q8jXLli1DUFBQ+yMuLq6vY5IH+aZQh4fXF8AqAXdM6I/HOVmVPNjI2CC8fV9a+22/8961LfZH5Eh2lZHw8HAoFArodLoOz+t0OkRFRXX6mujoaAwZMgQKxdlFo5KSkqDVamE0dj6Le+HChairq2t/lJeX2xOTqEvbDlfjwffyYbZKmJkSg2dmjmQRIY+XHBeMN387HmpvObYWV+GRD/fAYuXmeuQ4dpURpVKJ1NRUZGdntz9ntVqRnZ2N9PT0Tl8zadIkHDlyBFbr2aZ96NAhREdHQ6lUdvoalUqFwMDADg+ii7W7rAZz3/oZRrMV00Zo8PytyVBwHREiALZ1SFbdnQpvhQz/21OBJZ/v526/5DB2D9NkZWVh9erVWLt2LYqKijBv3jw0NjYiMzMTADBnzhwsXLiw/fh58+bhzJkzeOihh3Do0CFs3LgRS5cuxfz583vvqyC6gKNVDfjtm7vQbLJg8uBw/PuOMfDiyqpEHUwdGokVt6VAJgPe2VmGF74+JDoSeQi7d/6aNWsWqqqqsHjxYmi1WqSkpGDz5s3tk1rLysogl5/9IR8XF4evvvoKDz/8MEaPHo3Y2Fg89NBDePTRR3vvqyA6D52+BXNez0VNkwnJ/YKw6u5UqLy41wxRZ65PjoG+xYRFn+zHf747gmBfb9w/OUF0LHJzdq8zIgLXGaGeqms2YdYrOTiorcfAcD989Pt0hPmrRMcicnorvzuCf35VDAD49x1jcENyjOBE5Ir6ZJ0RIlfSYrJg7tqfcVBbj4gAFd767QQWEaJuenBqIu6dGA8A+PMHe7Cz5LTYQOTWWEbILVmtEh5eX4Dc0jMIUHlhbeYExIX6io5F5DJkMhmeuG44rhkRBaPFigfe+hmHdfWiY5GbYhkht/SPrw7iy/1aKBVyvDpnHIbHcHiPyF4KuQwv3p6C1AEh0LeYce8bu6DTt4iORW6IZYTczns/leGV70sAAM/dMhrpiWGCExG5LrW3AqvnjENCuB9O1jYj841daOCy8dTLWEbIrXx/qApPfLYfAPBwxhDMHMPdoYkuVqifEm9mTkC4vxKFp/T44/u7uSga9SqWEXIbB7V6zH83HxarhJvGxOKPVw4SHYnIbfQP88Xr94yHykuObw9WYvmXRaIjkRthGSG3UFnfgt+2Xj5OGxiKZTeP4jLvRL0sOS4YL9yWDABY/eMxrN9VJjgRuQuWEXJ5BrMFv387DxV1LUgI98Mrs7moGVFfuW50DP6UMRgAsOiT/cg5ylt+6eKxjJBLkyQJj3+yH/lltQhQe+G1e8Yh2LfzPY+IqHc8dOVgXJ8cA7NVwrx381Ba3Sg6Erk4lhFyaW9sL8WHeScglwH/uXMsEiL8RUcicnsymQz/vGU0UuKCUdtkwn1rd6G+xSQ6FrkwlhFyWT8ersIzGwsBAH+bnoQpQyIEJyLyHGpvBV6dk4roIDWOVjUi64M9sPIOG+ohlhFySceqG7Hgvd2wSsDNY/vhvksHio5E5HEiA9RYdXcqlF5ybCnU4aVvj4iORC6KZYRcTqPBjN+9/TPqmk0Y0z8Yz/5mJO+cIRIkOS4Yz84cCQD4v28O4ZtCneBE5IpYRsilSJKERz/ei0O6BkQGqPDK3alQe/POGSKRbh0XhznpAwAAD68vwNGqBsGJyNWwjJBLeWN7Kb7YewpechlW3jUWkYFq0ZGICMAT1w3HhPhQ1BvMeOCtnzmhlezCMkIuY1fpGSzdZFv18W/TkzA+PlRwIiJq462QY+VdYxEVaJvQ+ujHeyFJnNBK3cMyQi6hUt+CB9/Nh9kq4frkGGROihcdiYh+JSJAhZfvHgtvhQyb9mnx5o5S0ZHIRbCMkNMzWaxY8N5uVNUbMETjj+U3cal3Imc1pn8I/jY9CQDw7MYi5JfVCE5EroBlhJzeC18fQm7pGfirvLDq7lT4qbxERyKi87h3YjxmjIqG2Sphwbv5qGk0io5ETo5lhJzad8WVWPX9UQDAc7eM5gqrRC5AJpNh+c2jMDDcDxV1LXj4gwIuiEbnxTJCTktb14JHPtgDAJh9yQBMHxUtOBERdVeA2hv/vWssVF5ybC2uwn+3ckE06hrLCDkls8WKP67bjTONRgyPDsSiGUmiIxGRnZKiA/H0jbYF0VZsOYRdpWcEJyJnxTJCTunf2YeRe+wM/JQKrLxrLBc2I3JRt42Pw01jYmGVgIfe343aJs4foXOxjJDT2X6kGi99Z7uku/Qm27gzEbmup2aORHyYLyrqWvDYx/u4/gidg2WEnMqZRiP+tL4AkgTcMSEON6bEio5ERBfJX+WFl+6wrT+y+YAW7+WWiY5EToZlhJyGJEn460d7UVVvwKBIfyy+boToSETUS0b1C8Jfpw0DADz1v0Ic0tULTkTOhGWEnMZ7uWX4pkgHpUKOf92eAh8l54kQuZP7Lh2Iy4ZEwGC2YsF7+WgxWURHIifBMkJO4UhlA57+ohAA8NdrhmJETJDgRETU2+RyGV64NRnh/ioc0jW07zVFxDJCwhnNVjy0bjdaTFZcOigcv500UHQkIuojEQEqvHBbMgDgrZzj+P5QleBE5AxYRki4F7YU40CFHsG+3njhtmTI5dx3hsidTRkSgXvSBwAA/vLhHt7uSywjJFbO0dN49YcSAMDym0ZDE6gWnIiIHOGxa5OQEOGHynoDFn26n7f7ejiWERKmwWDGnz/cA0kCbh8fh2tGRomOREQO4qNU4MVZKfCSy7Bx7yl8vqdCdCQSiGWEhHl2YyFO1jajX4gPHr9uuOg4RORgo/sF4w9XDAYAPP7pflTUNgtORKKwjJAQ3xVX4v3ccgDA87cmw1/lJTgREYkw//JEJMcFo77FdqWUu/t6JpYRcri6JhMe+3gvAOC3kwbikoQwwYmISBQvhRwvzkqBj7cCO46exrtcndUjsYyQwz35vwPQ6Q1IiPDDX68ZKjoOEQk2MNwPj7b+LFi2qQjlZ5oEJyJHYxkhh9q8/xQ+2X0Schnwwq3J3I2XiAAAc9LjMSE+FE1GCx79eC/vrvEwLCPkMDWNRjz+6X4AwO+nJGJM/xDBiYjIWcjlMjx3y2ioveXYcfQ0N9PzMCwj5DBPf1GI6gYjhmj88VDGYNFxiMjJxIf7tW+mt3RjEU7UcLjGU7CMkEN8V1yJDa3DM/+4eTRUXhyeIaJz3TsxHuPjQ9BotOCxj/dxuMZDsIxQn6tvMWHRhn0AbHfPcHiGiLpiG65JhspLjm1HqrFuV7noSOQALCPU557bXIyKuhb0D/VF1tVDRMchIic3MNwPf5lmu7tm6aYiVOpbBCeivtajMrJy5UrEx8dDrVYjLS0Nubm5XR775ptvQiaTdXio1dx/xFPkHjuDt3ceBwAsv2kUfJVc3IyILixz0kCM7heE+hYznvzfAdFxqI/ZXUbWr1+PrKwsLFmyBPn5+UhOTsa0adNQWVnZ5WsCAwNx6tSp9sfx48cvKjS5hhaT7RY9ALhjQhwmDgoXnIiIXIVCLsPym0ZDIZdh0z4tthTqREeiPmR3GVmxYgXmzp2LzMxMDB8+HKtWrYKvry/WrFnT5WtkMhmioqLaHxqN5qJCk2t46dvDOFbdCE2gCo9dmyQ6DhG5mOExgZg7OQEA8MSn+1HfYhKciPqKXWXEaDQiLy8PGRkZZz+AXI6MjAzk5OR0+bqGhgYMGDAAcXFxuPHGG3HgwPkvuRkMBuj1+g4Pci2HdfV49YcSAMDfbxiJIB9vwYmIyBX9KWMwBoT5QqtvwfNfFYuOQ33ErjJSXV0Ni8VyzpUNjUYDrVbb6WuGDh2KNWvW4LPPPsM777wDq9WKiRMn4sSJE11+nmXLliEoKKj9ERcXZ09MEsxqlbDok/0wWSRkJGlwzcgo0ZGIyEWpvRV4duYoAMBbO48j73iN4ETUF/r8bpr09HTMmTMHKSkpmDJlCjZs2ICIiAi88sorXb5m4cKFqKura3+Ul/PWLlfyUd4J5Jaega9Sgb/fOEJ0HCJycZcODsfNY/tBkoCFG/bCZLGKjkS9zK4yEh4eDoVCAZ2u40QinU6HqKju/fbr7e2NMWPG4MiRI10eo1KpEBgY2OFBruF0gwFLvywCADycMQSxwT6CExGRO3h8RhJC/ZQ4pGvAmm3HRMehXmZXGVEqlUhNTUV2dnb7c1arFdnZ2UhPT+/Wx7BYLNi3bx+io6PtS0ouYemmg6htMmFYVADunRQvOg4RuYkQPyUWXmtbKv5f2YdRUdssOBH1JruHabKysrB69WqsXbsWRUVFmDdvHhobG5GZmQkAmDNnDhYuXNh+/FNPPYWvv/4aJSUlyM/Px913343jx4/j/vvv772vgpxCztHT+Dj/BGQyYOlNo+Ct4Jp6RNR7bh7bD+PjQ9BktODpLwpFx6FeZPcKVLNmzUJVVRUWL14MrVaLlJQUbN68uX1Sa1lZGeTys29CNTU1mDt3LrRaLUJCQpCamoodO3Zg+PDhvfdVkHBGsxWPf2pb8v3OCf0xlku+E1Evk8tleHrmSMz49zZ8uV+LrcWVmDo0UnQs6gUyyQV2IdLr9QgKCkJdXR3njzipV74/imVfHkS4vxLZj0zlrbxE1Gee+aIQr207hgFhvvjqT5dB7c2NN51Vd9+/eR2dLpq2rgX/yj4MAHjs2iQWESLqU3+6agg0gSocP92EVd8fFR2HegHLCF20pZuK0GS0YGz/YNw0JlZ0HCJyc/4qLzxxnW2o/79bj+L46UbBiehisYzQRdlZchqf76mATAY8deNIyOUy0ZGIyAPMGBWNyYPDYTRb8ff/cTKrq2MZoR4zW6xY8pltaf87J/THyNggwYmIyFPIZDI8ecMIeMll+PZgJb4r7nqzVnJ+LCPUY2/lHEexrh7Bvt7489VDRcchIg+TGOGPzNb1jJ7+XyGMZq7M6qpYRqhHquoN+L8thwAAf502DCF+SsGJiMgT/eHKwQj3V6KkuhFrd5SKjkM9xDJCPfL8V8WoN5gxKjYIs8ZzI0MiEiNQ7Y2/TrOtzPrv7MOoqjcITkQ9wTJCdjtQUYcP8mybFz55w3AoOGmViAS6JbUfRsUGod5gxvNfFYuOQz3AMkJ2kSQJT39RCEkCrk+OQeqAUNGRiMjDyeUyPHmD7VbfD/LKse9EneBEZC+WEbLL14U67Cw5A5WXHI9ew0mrROQcUgeEYmZKDCQJWPL5frjA4uL0Cywj1G0GswVLNxUBAOZOTkC/EF/BiYiIznrs2iT4KhXIL6vFF3tPiY5DdmAZoW57a8dxHD/dhIgAFeZNTRQdh4iog6ggNX4/xfaz6R+bD6LFZBGciLqLZYS65XSDAf9u3X/mL9OGwk9l94bPRER97v7JA6EJVOFETTPeyikVHYe6iWWEumXFlkOoN5gxIiYQt4ztJzoOEVGnfJVe7YswvvTtEdQ0GgUnou5gGaELOlJZj/dzywAAT1w3nPvPEJFTu2lsPyRFB6K+xdy+ozg5N5YRuqB/bC6GVQKuGq7BJQlhouMQEZ2XQi7DoulJAIB3dh7HsWru6uvsWEbovHaVnsGWQh0UchkevWaY6DhERN1y6eBwXD40AmarhH98eVB0HLoAlhHqkiRJ7bfy3jYuDoMi/QUnIiLqvoXTkyCXAZsPaJF77IzoOHQeLCPUpc37tdhdVgsfbwUezhgsOg4RkV2GaAJw+4T+AIClm4q4EJoTYxmhTpksVjzXusfD3MkDERmoFpyIiMh+f8oYDB9vBQrKa/F1oU50HOoCywh1at2uchyrbkSYnxIPTOECZ0TkmiID1Ljv0oEAgH9+VQyzxSo4EXWGZYTO0WAw41/fHAIA/PHKwfDnAmdE5MIemJKAYF9vHKlswIbdJ0XHoU6wjNA5XvuxBNUNRsSH+eKO1vFWIiJXFaj2xvypgwAAL245xGXinRDLCHVQ02jEaz8eAwA8cvVQKL34LUJErm92+gBEB6lRUdeCd3YeFx2HfoXvNNTBqu+PosFgRlJ0IGaMihYdh4ioV6i9FXg4YwgAYOV3R6BvMQlORL/EMkLtKvUtWNu6sdRfpg3hsu9E5FZuGhuLxAg/1DSZsPqHEtFx6BdYRqjdf747ghaTFWP7B+PyoZGi4xAR9SovhRx/mWZbSfq1H4+hqt4gOBG1YRkhAED5mab2zfD+Mm0YZDJeFSEi9zNthAbJccFoNlmw6vujouNQK5YRAgD8K/swTBYJlw4KR3oiN8MjIvckk8nwyFW2uSPv7DwOnb5FcCICWEYIsN17n38CAPDnaUMFpyEi6luTB4dj3IAQGMxW/Pe7I6LjEFhGCMD/fXMIVgm4argGKXHBouMQEfUpmUyGrKttV0fezy1HRW2z4ETEMuLhik7psXHvKchkwCOt/ziJiNzdxMRwXJIQCqPFiv/w6ohwLCMe7t/ZhwEA00dFY1hUoOA0RESOk3WVbVj6g13lKD/TJDiNZ2MZ8WAHtXp8uV8LmQx46MrBouMQETnUhIGhmDw4HGarhP98y6sjIrGMeLBfXhUZogkQnIaIyPH+1Loq60f5J1Ba3Sg4jediGfFQxdp6bNqnBQD88QpeFSEiz5Q6IARTh0bAYpXw728Pi47jsVhGPFTbVZEZo6IxNIpXRYjIc2W1rjvyWUEFjp/m1RERWEY8ULG2Hpv2nwIA/OHKQYLTEBGJNbpfMKYMsV0deXkrV2UVgWXEA/3728OQJGD6qCjeQUNEBOCPrb+YfZx/Aie57ojDsYx4mEO6emzaZ7sq8kfeQUNEBABIHRCKiYlhMFkkvMI9axyOZcTD/OfbI5Ak4NqRvCpCRPRLC66wXR1Zt6scldyzxqFYRjxIaXUjvthbAeDsPzoiIrJJTwjDuAEhMJqteOWHEtFxPEqPysjKlSsRHx8PtVqNtLQ05Obmdut169atg0wmw8yZM3vyaekivfLDUVgl4PKhERgREyQ6DhGRU5HJZPhD6/D1uz8dx+kGg+BEnsPuMrJ+/XpkZWVhyZIlyM/PR3JyMqZNm4bKysrzvq60tBR//vOfMXny5B6HpZ7T1rXgozzbzrzzL+dVESKizlw2OBzJ/YLQYrLitW3HRMfxGHaXkRUrVmDu3LnIzMzE8OHDsWrVKvj6+mLNmjVdvsZiseCuu+7C3//+dyQkJFxUYOqZ1T+WwGSRMGFgKMbFh4qOQ0TklGQyGRa0LgT51o5S1DYZBSfyDHaVEaPRiLy8PGRkZJz9AHI5MjIykJOT0+XrnnrqKURGRuK+++7r1ucxGAzQ6/UdHtRzZxqNeO+nMgDAg1MTBachInJuGUmRSIoORKPRgrdyjouO4xHsKiPV1dWwWCzQaDQdntdoNNBqtZ2+Ztu2bXj99dexevXqbn+eZcuWISgoqP0RFxdnT0z6lTe3H0OzyYIRMYGYMiRCdBwiIqcmk8kwr/UXtzd3lKLZaBGcyP316d009fX1mD17NlavXo3w8PBuv27hwoWoq6trf5SXl/dhSvdW32LCmztKAdjmishkMrGBiIhcwPSRUYgL9cGZRiM+zON7UF/zsufg8PBwKBQK6HS6Ds/rdDpERUWdc/zRo0dRWlqK66+/vv05q9Vq+8ReXiguLkZi4rnDBiqVCiqVyp5o1IV3fyqDvsWMhAg/TBtx7t8RERGdy0shxwOTE/DEZwfw6g8luHNCf3gpuBpGX7HrzCqVSqSmpiI7O7v9OavViuzsbKSnp59z/LBhw7Bv3z4UFBS0P2644QZcfvnlKCgo4PBLH2sxWfDaj7bZ4POmJEIh51URIqLuunVcHML8lDhR04yNrStXU9+w68oIAGRlZeGee+7BuHHjMGHCBLz44otobGxEZmYmAGDOnDmIjY3FsmXLoFarMXLkyA6vDw4OBoBznqfetyH/JKobDIgJUmPmmFjRcYiIXIraW4HMSfF4/utDWPV9CW5IjuFQdx+xu4zMmjULVVVVWLx4MbRaLVJSUrB58+b2Sa1lZWWQy3kpSzSrVcJrP9pWEPztpQPhzcuLRER2m31JPF7eehRFp/T4/lAVpg6NFB3JLckkSZJEh7gQvV6PoKAg1NXVITCQ+6l0x5ZCHea+9TMC1F7IWXgl/FV2904iIgLwzBeFeG3bMVySEIp1D5w7JYG61t33b/667KZe/cG26+RdaQNYRIiILsJ9kwfCWyHDzpIz2F1WIzqOW2IZcUP5ZTXYVVoDb4UMmZPiRcchInJp0UE+uDHFNu9u1fdHBadxTywjbmh1626TN6bEQhOoFpyGiMj1/X6KbSuTrwt1OH66UXAa98My4maOn27E5gO21XDnTuY+QEREvWFQZAAuHxoBSQLe2F4qOo7bYRlxM6/9eAySBEwdGoGhUQGi4xARuY37LrX9gvfBz+WoazYJTuNeWEbcyC+XLX6AV0WIiHrVpEFhGBYVgCajBetyy0THcSssI27knZ3H0WKyYmRsINITw0THISJyKzKZDPddOhCAbQM9k8UqOJH7YBlxEwbz2a2u505O4CqBRER94IaUGIT7q3CqrgWbuER8r2EZcRMb955CdYMBmkAVpo+KFh2HiMgtqbwUuCd9AADg9W3H4ALrhroElhE3IEkS1my3bYg3Jz2eS78TEfWhuy4ZAJWXHHtP1GFXKRdB6w1813IDPx+vwf6Teqi85LhjQn/RcYiI3FqonxI3je0HAO17gNHFYRlxA2+0XhWZmRKLUD+l4DRERO7vvkvjAQBbinQoreYiaBeLZcTFnaxtxlcHdACAzNZ/HERE1LcGRQZgausiaG03D1DPsYy4uLdySmGxSpiYGIZhUdzRmIjIUe6dGA8A+PDncjQazGLDuDiWERfWZDTj/Z9sC+9kThooOA0RkWe5bHAEBob7od5gxie7T4qO49JYRlzYhvyT0LeY0T/UF1cMixQdh4jIo8jlMsy+xHab71s5pbzN9yKwjLgoSZLw5o5SALZLhQo5FzkjInK0W8b1g69SgUO6BuQcPS06jstiGXFR24+cxpHKBvgpFbh1XD/RcYiIPFKg2hs3t97muzanVGwYF8Yy4qLe3lkKALgltR8C1N5iwxARebA5rSuybinU4URNk+A0rollxAWdqmvGlkLb7bx3t45XEhGRGIM1AZg0KAxWCXj3J+7m2xMsIy7o/Z/KYJWASxJCMVgTIDoOEZHHuyc9HgCwLrcMLSaL2DAuiGXExRjNVry/qxwAMPuSeLFhiIgIAHBlkgaxwT6oaTLh8z0VouO4HJYRF/N1oRZV9QZEBKhw9QiN6DhERARAIZdhdjpv8+0plhEX83brssN3TOjP3XmJiJzIrHFxUHrJsf+kHntP1ImO41L4buZCDunq8dOxM1DIZbhjQpzoOERE9AshfkrMGBUNAHiPE1ntwjLiQt7ZabsqclWSBtFBPoLTEBHRr92V1h8A8PmeCuhbTILTuA6WERfRYDBjQ75t74O2cUkiInIuqQNCMETjj2aTBZ9yv5puYxlxEZ/uPokGgxkJEX6YmBgmOg4REXVCJpPhrjTbL4zv7izjRNZuYhlxAZIktQ/R3JU2ADIZ96EhInJWM8fEQu0tR7GuHvllNaLjuASWERew50QdDmrrofSS4+axsaLjEBHReQT5eOP60TEAbFdH6MJYRlzA+l22b+bpI6MQ7KsUnIaIiC7krtatOr7Ydwq1TUbBaZwfy4iTazSY8XmBbTW/2yf0F5yGiIi6I7lfEIZHB8JotuKjvBOi4zg9lhEn9789FWg0WpAQ7oe0gaGi4xARUTfIZDLcdYntF8j3cjmR9UJYRpxc2z40s8bHceIqEZELuTElFn5KBUqqGrGz5IzoOE6NZcSJFZ3SY095LbzkMtw0tp/oOEREZAd/lRduSLHddNA29486xzLixNbl2r55rxquQUSASnAaIiKy16zxtq07vtyvRV0zV2TtCsuIk2oxWfBJ6+p9nLhKROSakvsFYagmAAazFf/bUyE6jtNiGXFSX+4/BX2LGbHBPpg8KFx0HCIi6gGZTIZbx9mG2T/4uVxwGufFMuKk3s89O3FVLufEVSIiV/WbMbHwVsiw90Qdik7pRcdxSiwjTqikqgG5x85ALkN7oyYiItcU5q9CRpIGAK+OdIVlxAm1LZAzZUgEooN8BKchIqKLdds420TWT3efhMFsEZzG+bCMOBmLVcKGfNvE1Vtbv3mJiMi1XTYkAlGBatQ0mfBNYaXoOE6nR2Vk5cqViI+Ph1qtRlpaGnJzc7s8dsOGDRg3bhyCg4Ph5+eHlJQUvP322z0O7O62H6mGVt+CIB9vXJkUKToOERH1AoVchptTbWuOcKjmXHaXkfXr1yMrKwtLlixBfn4+kpOTMW3aNFRWdt70QkNDsWjRIuTk5GDv3r3IzMxEZmYmvvrqq4sO747ahmhuTImBykshOA0REfWWW1NtV7t/OFyFitpmwWmci91lZMWKFZg7dy4yMzMxfPhwrFq1Cr6+vlizZk2nx0+dOhW/+c1vkJSUhMTERDz00EMYPXo0tm3bdtHh3U1dswlfHdACAG5J5cRVIiJ3Et+6x5gkAR9z87wO7CojRqMReXl5yMjIOPsB5HJkZGQgJyfngq+XJAnZ2dkoLi7GZZdd1uVxBoMBer2+w8MTbNx7CgazFUM0/hgVGyQ6DhER9bK2iawf5JVz87xfsKuMVFdXw2KxQKPRdHheo9FAq9V2+bq6ujr4+/tDqVRixowZeOmll3DVVVd1efyyZcsQFBTU/oiL84yJnB/l2cYRb0ntx03xiIjc0PRR0fBTKlB+phk/H68RHcdpOORumoCAABQUFGDXrl149tlnkZWVha1bt3Z5/MKFC1FXV9f+KC93/8k+R6sakF9WC4VchpmtGysREZF78VEqcO2oaADAhnwO1bTxsufg8PBwKBQK6HS6Ds/rdDpERUV1+Tq5XI5BgwYBAFJSUlBUVIRly5Zh6tSpnR6vUqmgUnnWxnAf/2JtkchAteA0RETUV24aE4uP8k7gi72nsOT6EVB782YFu66MKJVKpKamIjs7u/05q9WK7OxspKend/vjWK1WGAwGez61W7NYpfZN8ThxlYjIvV2SEIaYIDXqW8zILuKaI0APhmmysrKwevVqrF27FkVFRZg3bx4aGxuRmZkJAJgzZw4WLlzYfvyyZcuwZcsWlJSUoKioCC+88ALefvtt3H333b33Vbi4HUercaqOa4sQEXkCuVyGG8fYhuM/2c2hGsDOYRoAmDVrFqqqqrB48WJotVqkpKRg8+bN7ZNay8rKIJef7TiNjY148MEHceLECfj4+GDYsGF45513MGvWrN77Klwc1xYhIvIsN42Jxctbj2JrcRVONxgQ5u9ZUxN+TSa5wL1Fer0eQUFBqKurQ2BgoOg4varBYMa4Z7agxWTFp/MnISUuWHQkIiJygOtf2oZ9J+vw5PXDce+kgaLj9Inuvn9zbxrBvj6gRYvJioHhfkjux7VFiIg8xW/ah2pOCk4iHsuIYJ8WVACwDdFwbREiIs9xQ0oMFHIZ9pyow5HKBtFxhGIZEaiq3oDtR6oBgGuLEBF5mHB/FaYMiQDAiawsIwJt3FsBi1VCclww4sP9RMchIiIHu2ms7RfRT3dXwGp1+imcfYZlRKD2IZrkGMFJiIhIhIwkDQJUXjhZ24yfjp0RHUcYlhFBSqsbUVBeC7kMuC45WnQcIiISQO2twPTW5eE/K/DciawsI4J81npVZNKgcEQGcPl3IiJPdWOK7er4l/u1MJqtgtOIwTIigCRJ7Q2YE1eJiDxbWkIYIgJUqGs2YduRKtFxhGAZEWDfyTqUVDdC7S3HtJFdbzBIRETuTyGXYUbrUM3nrVfNPQ3LiACf7rZ9s2UkaeCvsntFfiIicjPXt97IsKVQh2ajRXAax2MZcTCLVcL/9trKCIdoiIgIAMb2D0ZssA8ajRZ8V+x5O/myjDhYztHTqKo3INjXG5e1LnZDRESeTSaTtV8d8cShGpYRB9u4z/ZNdu3IaCi9ePqJiMjmhtYy8m1xJepbTILTOBbfDR3IZLFi834tAOC60VxbhIiIzkqKDkBihB+MZiu2FOpEx3EolhEHyjl6GjVNJoT5KZE2MFR0HCIiciIdhmr2eNZQDcuIA23adwoAcM3IKHgpeOqJiKijtjKy7XA1zjQaBadxHL4jOojJYsXmA7YhmhkcoiEiok4kRvhjREwgzFapfVjfE7CMOMiOo6dR22RCuL8SaQPDRMchIiIndUP7UI3n7FXDMuIgG1vXFrlmZBQUcpngNERE5Kyuay0jPx07g8r6FsFpHINlxAFMFiu+OmCbGT1jVIzgNERE5Mxig32QEhcMSUL7e4e7YxlxgO1HqlHXbEK4vwoTeBcNERFdwLWt+5Zt3n9KcBLHYBlxgI17bd9M00dxiIaIiC7s2pG2Gx12lpzxiLtqWEb6mNFsxVdtd9GM4l00RER0Yf3DfDEiJhAWq4Qthe5/Vw3LSB/bfqQa+hYzIgJUGBfPIRoiIuqetqGaLz3gFl+WkT72RdsQDe+iISIiO1zTOlTTNu/QnbGM9CGTxdp+eW06h2iIiMgOgyL9MTjSHyaLhOwi976rhmWkD/1Ucgb6FjPC/JQcoiEiIrtd2/qLrLsP1bCM9KG2iatXDddwiIaIiOzWNm/k+0NVaDCYBafpOywjfcRqlfB16xDNtBFRgtMQEZErGhYVgPgwXxjNVnx3sFJ0nD7DMtJH9pyohU5vgJ9SgYmDuBcNERHZTyaTtU9kdeeN81hG+sjXhbbJRlOHRULlpRCchoiIXNX0Ubar698VV6LZaBGcpm+wjPSRtvkiHKIhIqKLMSo2CLHBPmgyWvD9oSrRcfoEy0gfOFJZj5KqRigVclw+NEJ0HCIicmG2oRrbL7ZfH3DPoRqWkT7QtsvixEFhCFB7C05DRESu7urhGgDAt8WVMFusgtP0PpaRPsAhGiIi6k2pA0IQ7OuN2iYT8o7XiI7T61hGellFbTP2nqiDTAZkJGlExyEiIjfgpZDjiqGRAIBv3HA1VpaRXral9S6a1P4hiAhQCU5DRETuIqN1qGZLoQ6SJAlO07tYRnoZh2iIiKgvXDYkAkqFHKWnm3C0qkF0nF7FMtKLahqN+OnYGQDA1SM4RENERL3HX+WF9ETbIppbCt1rNVaWkV70XXElLFYJw6ICMCDMT3QcIiJyM21DNe42b4RlpBdlt+4bwImrRETUFzKSbJNY88tqUN1gEJym9/SojKxcuRLx8fFQq9VIS0tDbm5ul8euXr0akydPRkhICEJCQpCRkXHe412VyWLFD8W2lfGuaP1mISIi6k3RQT4YGRsISQK+daON8+wuI+vXr0dWVhaWLFmC/Px8JCcnY9q0aais7PykbN26FXfccQe+++475OTkIC4uDldffTVOnjx50eGdyc+lNag3mBHmp0Ryv2DRcYiIyE21XX1vu3vTHdhdRlasWIG5c+ciMzMTw4cPx6pVq+Dr64s1a9Z0evy7776LBx98ECkpKRg2bBhee+01WK1WZGdnX3R4Z/LtQds3xZShEVDIZYLTEBGRu2orIz8erkKLyT02zrOrjBiNRuTl5SEjI+PsB5DLkZGRgZycnG59jKamJphMJoSGhtqX1Mm1XS67chjnixARUd8ZEROImCA1WkxWbD9SLTpOr7CrjFRXV8NisUCj6fiGq9FooNV2b/OeRx99FDExMR0Kza8ZDAbo9foOD2d2/HQjjlY1wksuw+Qh4aLjEBGRG5PJZG53V41D76ZZvnw51q1bh08++QRqtbrL45YtW4agoKD2R1xcnANT2q/tqsi4+BAEcmM8IiLqY21DNd8UVcJqdf3VWO0qI+Hh4VAoFNDpOjYxnU6HqKjzrzj6/PPPY/ny5fj6668xevTo8x67cOFC1NXVtT/Ky8vtielwHKIhIiJHSksIhZ9Sgap6A/ZX1ImOc9HsKiNKpRKpqakdJp+2TUZNT0/v8nXPPfccnn76aWzevBnjxo274OdRqVQIDAzs8HBWDQYzfiqxrbp6+TDe0ktERH1P5aXApEG2aQFbW5eVcGV2D9NkZWVh9erVWLt2LYqKijBv3jw0NjYiMzMTADBnzhwsXLiw/fh//OMfeOKJJ7BmzRrEx8dDq9VCq9WiocE91tXfdrgaRosVA8J8kRjBVVeJiMgxprbu4vv9IdcvI172vmDWrFmoqqrC4sWLodVqkZKSgs2bN7dPai0rK4NcfrbjvPzyyzAajbjllls6fJwlS5bgySefvLj0TuC71iGay4dGQibjLb1EROQYU4ZGAAB2l9WgtsmIYF+l4EQ9Z3cZAYAFCxZgwYIFnf7Z1q1bO/x/aWlpTz6FS7BaJXxb3DpfhKuuEhGRA8UG+2BwpD8OVzbgx8PVuD45RnSkHuPeNBfhQIUeVfUG+CoVmDDQvdZNISIi5ze19eqIqw/VsIxchOzWVVcnDw6HykshOA0REXmaX84bceVbfFlGLkLbfJEreBcNEREJMC4+BL6tt/gWnnLuBULPh2Wkh043GLD3pO3e7rZmSkRE5EgqLwUmJoYBcO2hGpaRHtp+9DQkCRgWFQBNYNeryRIREfWlKW1DNS683gjLSA/92NpAJw/mXjRERCTO1CG2Sax5ZTWoazYJTtMzLCM9IEkSfjxs2ylx8uAIwWmIiMiTxYXaFt20WCWX3cWXZaQHjlY1QKtvgdJLzlt6iYhIuKkuPlTDMtIDPxyyNc+0gaFQe/OWXiIiEmvKkLPrjUiS693iyzLSAz8e5nwRIiJyHhMGhsLHWwGtvgUHtfWi49iNZcROBrMFO1t36eV8ESIicgZqbwXSW2/xdcVdfFlG7JR3vAbNJgvC/VUYFhUgOg4RERGAs0M1246wjLi9trtoLhsczl16iYjIaUwaZJs68HNpDVpMFsFp7MMyYqf2+SJDOF+EiIicR2KEHzSBKhjMVuQfrxEdxy4sI3Y43WDA/pO2tf/bGigREZEzkMlkmJRoe2/aftS11hthGbHDttbFZJKiAxEZwCXgiYjIuUxs/UV525HTgpPYh2XEDr+cL0JERORsJg2y3VGz70StSy0NzzLSTbYl4NvWF+EtvURE5Hyig3yQEO4HqwT8VOI6V0dYRrrpcGUDdHoDVF5yjIsPER2HiIioUxNbr47sOMoy4nbahmgmcAl4IiJyYu2TWF1o0zyWkW7a2Xq5i3fREBGRM0tPDINMZruiX6lvER2nW1hGusFqlZB7zLYE/CUJYYLTEBERdS3YV4kRMYEAXGeohmWkG4q0etQ1m+CnVGBk618wERGRs3K1oRqWkW5o2xhv/MBQeCl4yoiIyLm1rTey4+hpSJIkOM2F8Z21G9rmi3CIhoiIXMH4+BB4K2Q4WduM46ebRMe5IJaRC+B8ESIicjW+Si+MibMtQ+EKS8OzjFwA54sQEZEraltvxBXmjbCMXADnixARkStqW4oi5+hpWK3OPW+E764XwPkiRETkilLiguGrVKCmyYQirV50nPNiGTkPzhchIiJX5a2QI3WAbd5I23uZs2IZOQ/OFyEiIlfW9os0y4gL43wRIiJyZRMGhgKwlRFnXm+E77DnwfkiRETkykb3C4LKS47TjUYcrWoQHadLLCNd4HwRIiJydSovBcb2t80babva74xYRrrA+SJEROQOfjlU46xYRrrA+SJEROQO0hKcf94I32W7wPkiRETkDsbE2fap0epbUHbGOfepYRnpBOeLEBGRu/BRKpDcLxgA8JOTzhthGenE4coG1DWb4OOtwAjOFyEiIhc3Lt42VPPzcZYRl9H2l5USFwxvzhchIiIXN651Jdafj9cITtI5vtN2Iq/U9pc1Lj5EcBIiIqKL17YsfElVI840GgWnORfLSCfammPbXx4REZErC/FTYlCkPwAgzwmvjvSojKxcuRLx8fFQq9VIS0tDbm5ul8ceOHAAN998M+Lj4yGTyfDiiy/2NKtDVNbbZhvLZMBYlhEiInITZ4dqnG/eiN1lZP369cjKysKSJUuQn5+P5ORkTJs2DZWVlZ0e39TUhISEBCxfvhxRUVEXHbivtQ3RDNUEIFDtLTgNERFR72i72t/2PudM7C4jK1aswNy5c5GZmYnhw4dj1apV8PX1xZo1azo9fvz48fjnP/+J22+/HSqV6qID97W2IRrOFyEiInfSdkfN3pN1MJgtgtN0ZFcZMRqNyMvLQ0ZGxtkPIJcjIyMDOTk5vRbKYDBAr9d3eDhKexkZEOqwz0lERNTX4sN8EeanhNFsxf6Tjntf7Q67ykh1dTUsFgs0Gk2H5zUaDbRaba+FWrZsGYKCgtofcXFxvfaxz6fZaMGBk3UAOHmViIjci0wmOztU42TzRpzybpqFCxeirq6u/VFeXu6Qz7v3RC3MVgmaQBX6hfg45HMSERE5StsUhJ+dbN6Ilz0Hh4eHQ6FQQKfTdXhep9P16uRUlUolZH7J7vJaALZ1/GUymcM/PxERUV8a099WRnaX10KSJKd5r7PryohSqURqaiqys7Pbn7NarcjOzkZ6enqvh3O03WW2pjimf7DYIERERH1gZEwQvOQyVNUbUFHXIjpOO7uHabKysrB69WqsXbsWRUVFmDdvHhobG5GZmQkAmDNnDhYuXNh+vNFoREFBAQoKCmA0GnHy5EkUFBTgyJEjvfdV9JKC1isjKXHBQnMQERH1BR+lAsOiAwAABWW1YsP8gl3DNAAwa9YsVFVVYfHixdBqtUhJScHmzZvbJ7WWlZVBLj/bcSoqKjBmzJj2/3/++efx/PPPY8qUKdi6devFfwW95FRdM3R6AxRyGUb1CxIdh4iIqE+kxAVj/0k9CsprMGN0tOg4AHpQRgBgwYIFWLBgQad/9uuCER8fD0mSevJpHKqtIQ7VBMBX2aPTQkRE5PTGxIXgnZ1l7aMBzsAp76YRoW3yagrnixARkRtre5/be6IOJotVbJhWLCOt2q6McL4IERG5s4FhfghUe8FgtqJYWy86DgCWEQCA2WLF3pO1AIAxLCNEROTG5HIZklvf63Y7yVANywiAg9p6tJisCFB5ITHCX3QcIiKiPtW+3kiZcyx+xjKCs7f0JscFQy53jgVgiIiI+krbKICzTGJlGYFtGXgASI7jLb1EROT+2oZpSqoaoW8xiQ0DlhEAwL7W3QtHxbKMEBGR+wv1UyI22LYH2wEn2MHX48tIi8mCwzrbbOKRLCNEROQhRsYGAgD2t+5WL5LHl5GD2nqYrRJCfL3bWyIREZG7axsN2McyIl7bX8LI2CCn2b2QiIior7WNBvDKiBPYf8L2l8D5IkRE5Ena3vdKqhtRL3gSq8eXkbYrI6O5OR4REXmQMH/V2UmsFWInsXp0GWkxWXCIk1eJiMhDOcskVo8uI4d0nLxKRESey1kmsXp0GeHkVSIi8mQjWUbEa7ssxcmrRETkidre/45VN6LBYBaWw6PLyD6WESIi8mBh/irEBKkhScABgVdHvIR9ZieQOXEgdpfXIKV/sOgoREREQsyZGA+LVUKMwLmTMkmSJGGfvZv0ej2CgoJQV1eHwMBA0XGIiIioG7r7/u3RwzREREQkHssIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQklJfoAN3RtrGwXq8XnISIiIi6q+19u+19vCsuUUbq6+sBAHFxcYKTEBERkb3q6+sRFBTU5Z/LpAvVFSdgtVpRUVGBgIAAyGSyHn8cvV6PuLg4lJeXIzAwsBcTUmd4vh2L59uxeL4di+fbsXrrfEuShPr6esTExEAu73pmiEtcGZHL5ejXr1+vfbzAwEB+MzsQz7dj8Xw7Fs+3Y/F8O1ZvnO/zXRFpwwmsREREJBTLCBEREQnlUWVEpVJhyZIlUKlUoqN4BJ5vx+L5diyeb8fi+XYsR59vl5jASkRERO7Lo66MEBERkfNhGSEiIiKhWEaIiIhIKJYRIiIiEsrtysjKlSsRHx8PtVqNtLQ05Obmnvf4Dz/8EMOGDYNarcaoUaOwadMmByV1D/ac79WrV2Py5MkICQlBSEgIMjIyLvj3Qx3Z+/3dZt26dZDJZJg5c2bfBnQz9p7v2tpazJ8/H9HR0VCpVBgyZAh/ptjB3vP94osvYujQofDx8UFcXBwefvhhtLS0OCit6/rhhx9w/fXXIyYmBjKZDJ9++ukFX7N161aMHTsWKpUKgwYNwptvvtm7oSQ3sm7dOkmpVEpr1qyRDhw4IM2dO1cKDg6WdDpdp8dv375dUigU0nPPPScVFhZKjz/+uOTt7S3t27fPwcldk73n+84775RWrlwp7d69WyoqKpLuvfdeKSgoSDpx4oSDk7sme893m2PHjkmxsbHS5MmTpRtvvNExYd2AvefbYDBI48aNk6ZPny5t27ZNOnbsmLR161apoKDAwcldk73n+91335VUKpX07rvvSseOHZO++uorKTo6Wnr44YcdnNz1bNq0SVq0aJG0YcMGCYD0ySefnPf4kpISydfXV8rKypIKCwull156SVIoFNLmzZt7LZNblZEJEyZI8+fPb/9/i8UixcTESMuWLev0+Ntuu02aMWNGh+fS0tKk3/3ud32a013Ye75/zWw2SwEBAdLatWv7KqJb6cn5NpvN0sSJE6XXXntNuueee1hG7GDv+X755ZelhIQEyWg0OiqiW7H3fM+fP1+64oorOjyXlZUlTZo0qU9zupvulJG//vWv0ogRIzo8N2vWLGnatGm9lsNthmmMRiPy8vKQkZHR/pxcLkdGRgZycnI6fU1OTk6H4wFg2rRpXR5PZ/XkfP9aU1MTTCYTQkND+yqm2+jp+X7qqacQGRmJ++67zxEx3UZPzvfnn3+O9PR0zJ8/HxqNBiNHjsTSpUthsVgcFdtl9eR8T5w4EXl5ee1DOSUlJdi0aROmT5/ukMyexBHvlS6xUV53VFdXw2KxQKPRdHheo9Hg4MGDnb5Gq9V2erxWq+2znO6iJ+f71x599FHExMSc801O5+rJ+d62bRtef/11FBQUOCChe+nJ+S4pKcG3336Lu+66C5s2bcKRI0fw4IMPwmQyYcmSJY6I7bJ6cr7vvPNOVFdX49JLL4UkSTCbzfj973+Pv/3tb46I7FG6eq/U6/Vobm6Gj4/PRX8Ot7kyQq5l+fLlWLduHT755BOo1WrRcdxOfX09Zs+ejdWrVyM8PFx0HI9gtVoRGRmJV199FampqZg1axYWLVqEVatWiY7mlrZu3YqlS5fiv//9L/Lz87FhwwZs3LgRTz/9tOho1ANuc2UkPDwcCoUCOp2uw/M6nQ5RUVGdviYqKsqu4+msnpzvNs8//zyWL1+Ob775BqNHj+7LmG7D3vN99OhRlJaW4vrrr29/zmq1AgC8vLxQXFyMxMTEvg3twnry/R0dHQ1vb28oFIr255KSkqDVamE0GqFUKvs0syvryfl+4oknMHv2bNx///0AgFGjRqGxsREPPPAAFi1aBLmcv2v3lq7eKwMDA3vlqgjgRldGlEolUlNTkZ2d3f6c1WpFdnY20tPTO31Nenp6h+MBYMuWLV0eT2f15HwDwHPPPYenn34amzdvxrhx4xwR1S3Ye76HDRuGffv2oaCgoP1xww034PLLL0dBQQHi4uIcGd/l9OT7e9KkSThy5Eh76QOAQ4cOITo6mkXkAnpyvpuams4pHG1FUOKWa73KIe+VvTYV1gmsW7dOUqlU0ptvvikVFhZKDzzwgBQcHCxptVpJkiRp9uzZ0mOPPdZ+/Pbt2yUvLy/p+eefl4qKiqQlS5bw1l472Hu+ly9fLimVSumjjz6STp061f6or68X9SW4FHvP96/xbhr72Hu+y8rKpICAAGnBggVScXGx9MUXX0iRkZHSM888I+pLcCn2nu8lS5ZIAQEB0vvvvy+VlJRIX3/9tZSYmCjddtttor4El1FfXy/t3r1b2r17twRAWrFihbR7927p+PHjkiRJ0mOPPSbNnj27/fi2W3v/8pe/SEVFRdLKlSt5a++FvPTSS1L//v0lpVIpTZgwQdq5c2f7n02ZMkW65557Ohz/wQcfSEOGDJGUSqU0YsQIaePGjQ5O7NrsOd8DBgyQAJzzWLJkieODuyh7v79/iWXEfvae7x07dkhpaWmSSqWSEhISpGeffVYym80OTu267DnfJpNJevLJJ6XExERJrVZLcXFx0oMPPijV1NQ4PriL+e677zr9Wdx2fu+55x5pypQp57wmJSVFUiqVUkJCgvTGG2/0aiaZJPF6FhEREYnjNnNGiIiIyDWxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCfX/2+ckXupPPKkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0.01,0.99,200)#范围0.01-0.99\n",
    "plt.plot(x,entropy(x))\n",
    "plt.show()#x0.5时，最不稳定，当->0or->1时，变得稳定 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
